The electron density distribution in electron beams produced in high‐current field‐emission diodes often shows striations in the form of periodic maxima and minima. The nature of the striations depends on the shape of the cathode. A theory of these striations applicable to cylindrical cathodes is given. The current is taken to be flowing through the cathode flare plasma formed in the diode during the course of beam emission and the stability of such a current‐carrying plasma is studied. For certain wavelengths of perturbation, the perturbation grows exponentially and leads to an instability which manifests itself as striations in the current distribution. The unstable wavelengths are related to the characteristic dimensions of the cathode.